Every day, scientists make discoveries that change the way we live. But sometimes, just sometimes, they achieve results that are so extraordinary or unexpected that they literally don't know what to do with them. Here are five of the most puzzling.

Mind-bending material properties

In January, a team of physicists from Rutgers and MIT published a paper in Nature describing a new property of matter. While fiddling around with a super-cooled Uranium compound, URu2Si2, they found that it breaks something called double time-reversal symmetry. Normal time-reversal symmetry states that the motion of particles looks the same running back and forth in time: magnets break that, though, because if you reverse time, the magnetic field they produce reverses direction. You have to reverse time twice to get them back to their original state.

This new material, though, breaks double time-reversal symmetry. That means you need to reverse time four times for the behaviour to get back to its original state. It's something the scientists have dubbed hastatic order — and if you're struggling to get your head round it, well, that's the appropriate reaction. The scientists who discovered the phenomenon can't explain a good physical example of what it is, how it works, or what it means. One to keep on the back burner, then.

The universe weighs less than we thought

When the world's best scientists decided to team up and measure the mass of the universe all the way back in the 1970s, they set themselves a pretty tall challenge. Applying their best understanding of gravity and the dynamics of galaxies, though, they came up with an answer — an answer which sadly predicts our universe should be falling apart. We know that the Universe's galaxies' matter orbits a single central point — we've observed it! — and that must mean their own motion generates enough centripetal force to make that happen.

But calculations suggest that there's not actually enough mass in the galaxies to produce the forces required to keep themselves moving in the way we've observed. So physicists scratched their heads, worried a little, then proudly stated that there must be more stuff out there than we can see. That's the theory behind what everyone now refers to as Dark Matter. The only problem? In the past 40 years, nobody has confirmed whether it really exists or not—so, effectively, the problem thrown up by those initial calculations remains.

The placebo effect

Feed a sick man a dummy pill that he thinks will cure him and, often, his health will improve in a similar way to someone taking real drugs. In other words, a bunch of nothing can improve your health. In theory, it could be a powerful treatment technique.

But experiments have shown that the kind of nothing you deliver matters: when placebos are laced with a drug that blocks the effects of morphine, for instance, the effect vanishes. While that proves that the placebo effect is somehow biochemical—and not just a psychological effect—we know practically nothing else about the power of placebo.

It's real, sure. It can help people get better, agreed. But if we're ever to make anything of the much-studied but little-understood effect, we're going to have to unpick how the mind can affect the body's biochemistry—and, right now, nobody knows.

Temperatures below absolute zero

It used to be that scientists all agreed that it was impossible to achieve temperatures below absolute zero. It was literally the coldest anything could ever get. Late last year, though, a team of scientists from the Max-Planck-Institute in Germany blew that out of the water: finally, they'd cooled a cloud of gas atoms to below −273.15°C. In fact, the result was as much a quirk of the definition of temperature as anything else, and the way it relies on both energy and entropy (the measure of disorder of particles). New Scientist explains:

In principle [it's] possible to keep heating the particles up, while driving their entropy down. Because this breaks the energy-entropy correlation, it marks the start of the negative temperature scale, where the distribution of energies is reversed – instead of most particles having a low energy and a few having a high, most have a high energy and just a few have a low energy.

It's this curious logic that allowed the Max-Planck-Institute researchers to cool a variety of atoms in a vacuum, for the first time ever, to below absolute zero. So far, though, they haven't managed to work out what to do with the chilled particles.

Cold fusion

Back in 1989, a pair of scientists—Fleischmann and Pons—claimed that they'd achieved a remarkable feat: they'd successfully observed nuclear fusion at room temperatures. Momentarily, the finding was heralded as a revolutionary discovery that could transform energy production around the globe. Sadly, their experiments weren't reproducible—but they did inspire scientists to study cold fusion in more depth.

Turns out, the process is in fact theoretically possible. For two atoms two fuse together, they need to come close enough to each other to overcome their mutual electric repulsion, which is caused by the cloud of electrons that orbit them. Usually that's made possible by super-high temperatures—like at the center of the sun—but quantum physics suggests that, because the position of the electric field causing the repulsion is probabilistic, there is at least the possibility that atoms can fuse without the need for energy injection via high temperatures.

And it's that hope that means a small band of scientists still work in the shadows, trying to get cold fusion to work. Of course, while occasional results come and go, they tend to be rather dubious. Fundamentally that's because, even though quantum theory tells us it should be possible, nobody knows how to use that understanding to actually get a fusion reaction going.